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On a mean field game approach modeling congestion and aversion in pedestrian crowds

Abstract : In this paper we present a new class of pedestrian crowd models based on the mean field games theory introduced by Lasry and Lions in 2006. This macroscopic approach is based on a microscopic model, that considers smart pedestrians who rationally interact and anticipate the future. This leads to a forward-backward structure in time. We focus on two-population interactions and validate the modeling with simple examples such as self-organization behavior as for instance lane formation. Two complementary classes of problems are addressed, namely the case of crowd aversion and the one of congestion. In both cases we describe the model, build a numerical solver (respectively based on optimization formulation and partial differential equations), and finally provide some numerical tests involving complex group behaviors such as symmetry breaking and lane formation.
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https://hal.archives-ouvertes.fr/hal-00554898
Contributor : Aimé Lachapelle Connect in order to contact the contributor
Submitted on : Tuesday, January 11, 2011 - 4:24:52 PM
Last modification on : Saturday, April 11, 2020 - 6:38:03 PM
Long-term archiving on: : Monday, November 5, 2012 - 4:15:50 PM

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  • HAL Id : hal-00554898, version 1

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Aimé Lachapelle, Marie-Thérèse Wolfram. On a mean field game approach modeling congestion and aversion in pedestrian crowds. 2011. ⟨hal-00554898⟩

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